Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 705 · Overbeck, fol. 25r

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.93.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 24v); this page is its right half.

The machine reads it as

  1. Aliud Exemplum: Quaeratur linea undecima
  2. numerum Lateris,
  3. Resolvo 11. = 8 +2 +1., quae partes metratur 16 per Quotietes, 2. 8. 16.
  4. Ergo colligo Progressiones 0. 1. 0. 1. Iten 0. 1. 2. 3. 4. 5. 6. 7. 0. 1. etc:
  5. _ 3. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1. 12. 13. 14. 15.
  6. 16.
  7. Et facto Denominatore comuno 16
  8. pono 8. B, 0. 8, 0. 8. 0, 8. 0. 8. 0. 8. 0. 8. 0. 8
  9. 0. 2. 4, 6. 8, 10, 12. 14. 0. 2. 4. 6. 8. 10. 12. 19
  10. 3.
  11. 1. 2
  12. 5. 6.
  13. 8. 9. 50. B. 12. 13. 14 15
  14. Suma v. 1. 6. 17. 12. 23. 10. 19. 8. 19. 14. 25. 20. 31. 26, 37
  15. Lineam in pleno systemate Periodi Summativae
  16. Quaeratur Linea Abaci ex Problemate H
  17. Qualis autem Abacus sumi debeat Canon paulo ante Problemal. indicabit
  18. Singula membra Abaci multiplicentur pen quadruplum Numerum Lateri
  19. Si Numerus Columnae desinat in 1. ut 21. 31. qi’ etc:) dt inveta finea bis reponitu
  20. At si Numer: Colu. desinat in 0. ut 10. 26. 30. 40. etci singula membra
  21. Lineae inventae multiplicentur per octuplum Numerum Lateris Abaci e in
  22. venta Linea quater reponetur
  23. ut in Coluna va petitur Linea devigesima secunda. Seu Portio 22.
  24. Z + -1. - 32. tot mebra sunt in Latere Abaci quo indigeo. Ergo 32. Numerus
  25. Laleris paratus est.
  26. Et quia poscitur Lortio 22. resolvo hoc in 16. 4. 2
  27. e dividendo Numerum Lateris 32. per has discerptiones repono Quotietes 2. 6. 16
  28. e sumo Progressiones 1. pro 2.
  29. 0. 1. 2. 3. 4. 5. 6. 2. pro 8.
  30. et 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1.
  31. 8, 12. 13 14. 15. pro 16.
  32. Sed omnium earum Progressionum Communis Denominator debet esse 32. aquali
  33. perpetuo ipsi Numero Lateris in Abaco cujus Linea quaeritur
  34. Ergo vario Numeratores, ita ut valores quadrent ad Denominatorem. Con
  35. munem 32. d scribo eas Progressiones hac serie
  36. pro Quotiete 2. Progr. 0. 16. 0. 16. 0. 16, 0.16. 8. 16, 9. 16. 0. 16, 9. 15, 0. 16, 0. 16. 0. 16, 0. 16. 0. 16, 0. 16. 0. 16. 0. 16
  37. 8 1 0. 4. 8. 12. 16, 20. 24. 28. 8. 4. 8. 12. 16, 20, 24, 28. 8. 4. 8, 12. 16. 20. 2928. 0, 4. 8. 12. 16, 20, 24, 28
  38. 16 a 0. 2. 4. 6. 8. 10, 12, 14. 16, 18, 20. 22. 24. 26.28, 30, 0, 2.4, 6. 8, 10, 12. 14,16, 18, 20, 22. 24, 26,29, 24
  39. 0. 22. 12. 34. 24. 46. 36. 58. 16. 38. 28. 50. 40. 62. 52. 74, 0. 22. 1234. 2946.36. 58. 16. 38. 28, 50. 40. 62, 52. 79
  40. Sed hoc inventum bis reponendum est
  41. ac (6. 22. 12. 3424. 46., 36. 58. 16. 38. 28. 50, 40. 62. 52. 74. 0. 22. 12. 3424. 46. 16.58.16. 38. 28. 50. 40. 62. 52. 74022.12. 3+ 29 46. 16 58. 16. 38. 285040 b2 52. 74. 02 2 12. 34 24. 46 365816.3 4. 28. 50. qubrpe
  42. Hujus inventae Lineae singula membra oportebit multiplicari per quadruplum Numerum Lateris
  43. seu per 128. et denique singulis (mebris suu eoadratum addi quibus Quadrati
  44. supra spoliavi omnia mebra ut in hac nuditate mebrorum progressionem certive
  45. prehenderem. Sic membro quod ordine est 19 num addi debet Qvadratum
  46. Numeri 19 seu 361. et sic in aliis.
  47. Quae operationes si Actu ipso non ita commode institui possint mihi tamen satis est
  48. primo probasse quod res sit in potertate nostra, ut extra seriem ad quamvis
  49. Columnam possimus exhibere desiverata Portionem in Percodo Summativa
  50. Posteaquam vero probatum est periodos sumativas extra feriem, esse in potestate
  51. etiam probavi quoo ipsa Periodi suet in potestate extra seriem.
  52. Nam
  53. si summativa detrahas summatioa proxime inferiorem, Residuum est
  54. quaesita Periodus sed ne hoc quidem opus est, quia quicquid ab inferioribu
  55. ultra debitum ad superiora additum est, id totum in Fractionibus subsistit ut tam
  56. facile sit distinguere puram Columnam ab additis inferioribus, quam facile est
  57. integra a Fractionibus dignoscere
  58. Exemplo sit supra inventa Colamna zi summata quam sic expresserama
  59. 0. 1. 4. 9. 16, 25. 36. 49, 0. 17. 36. 57. 16, 41. 68. 97. 0. 33. 4. 41. 16.57. 36, 81. 0. 49, 36, 89. 16. 73, 68, 129
  60. evaritur hinc Col. 21. e
  61. 13C. solitare
  62. per 32. missis Residuis et ex serie Quotorum fiat Periodus Col. 21 solitaria
  63. ut 0. 0. 0. 0,0,0. 1, 1. 0. 0. 1. 1. 0, 1. 2. 3, 0. 1. 0. 1. 0, 1. D. 2. 0. 1. 1. 2. 0, 2. 2. 4
  64. Expurgado, v. 8. 8. 0. 0, 0. 1. L. 0. 0, 1. 1. 0 1. 8. 1. 0. 1. 0. 1. 0. 1. 1. 0. 8. 1. 1, 0. 0. 8. 0. 0
  65. se facile bata periodo summata ernitur vera Percodus.

Cite

LBr. 705 · Overbeck, fol. 25r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-861255:0049?run=74